This condition ensures the existence of the limit of slope parameters which are often referred to as “quasi-true” parameters [1]}, and similar conditions are imposed in many model averaging studies, such as [2]}, [3]}, among others.
Further, we denote
\({\mu }^*_{(s)}= {\bf K}_{(s)}(\beta ^\ast _{(s)}){\bf y}\)  and \(\widetilde{{\mu }}^*_{(s)}= \widetilde{{\bf K}}_{(s)}({\bf 1}_{J_n}\otimes \beta ^\ast _{(s)}){\bf y}\) , where \(\otimes \)  denotes the Kronecker product and \({\bf 1}_{J_n}\)  is a \(J_n\times 1\)  vector of 1.
